In high energy physics (HEP), machine learning methods have emerged as an effective way to accurately simulate particle collisions at the Large Hadron Collider (LHC). The message passing generative adversarial network (MPGAN) was the first model to simulate collisions as point, or particle'' clouds, with state-of-the-art results, but suffered from quadratic time complexity. Recently, generative adversarial particle transformers (GAPT) were introduced to address this drawback; however, results did not surpass MPGAN. We introduce induced GAPT (iGAPT) which, by integratinginduced particle-attention blocks'' and conditioning on global jet attributes, not only offers linear time complexity but is also able to capture intricate jet substructure, surpassing MPGAN in many metrics. Our experiments demonstrate the potential of iGAPT to simulate complex HEP data accurately and efficiently.